Variable Domain Decomposition And Movable Boundary Control In Thermodynamic Sea Ice Model

In view of problems on solving parabolic equation with piecewise-differentiability, parameter identification on the problems is discussed in this paper by non-overlapping domain decomposition method. Main theoretic results are as following.1.Through introducing an energy transmission function on internal boundary, a distributed parameter identification model is established. In the model state variable is temperature in subdomains, and identification variable is the energy transmission function,temperature,thickness of the snow and ice. Its objective functional is to minimize the sum of the difference between temperatures on the interfaces among all neighbor subdomains.2.The movable boundary problem is transformed into immovable boundary problem byusing time variable-mesh method,so the numerical calculation is convenient. -3.The existence of the of the system's generalized solutions and the sub-system's solutions and the continuity of the solutions to the identification variable are proved using the theories of the partial-differential equation's solutions and the existence of the piecewise-differential system's solutions.Results above are applied to calculation of temperature field in the thermodynamic sea ice model. According to the special condition of the sea ice, the calculated domain is divided into three parts,which are the snow part,the ice part and the sea water part. So the system in the each part is differential.In order to solve the problem of the movable boundary in each part,the time variable-mesh method is used. And the sub-system is changed correspondingly. Based on the numerical simulation algorithm in this paper, numerical results for temperature field are given and analyzed. The results show that the numerical simulation is coincident with the experiments, and that the mathematical model and the domain decomposition method in this paper are corrective and effective.